Find sin() and cos(), tan() and cot(), and sec() and csc(). webassign plot (a) sin() and cos() (b) tan() and cot() (c) sec() and
1 answer:
The values of the trigonometry functions are sin(α) = 4/7, cos(β) = 4/7, tan(α) = 4/√33, cot(β) = 4/√33, sec(α) = 7/√33 and sec(β) = 7/√4
<h3>How to evaluate the trigonometry functions?</h3>The figure that completes the question is added as an attachment
From the figure, we have the third side of the triangle to be
Third = √(7^2 - 4^2)
Evaluate
Third = √33
The sin(α) is calculated as:
sin(α) = Opposite/Hypotenuse
This gives
sin(α) = 4/7
The cos(β) is calculated as:
cos(β) = Adjacent/Hypotenuse
This gives
cos(β) = 4/7
The tan(α) is calculated as:
tan(α) = Opposite/Adjacent
This gives
tan(α) = 4/√33
The cot(β) is calculated as:
cot(β) = Adjacent/Opposite
This gives
cot(β) = 4/√33
The sec(α) is calculated as:
sec(α) = Hypotenuse/Adjacent
This gives
sec(α) = 7/√33
The csc(β) is calculated as:
sec(β) = Hypotenuse/Opposite
This gives
sec(β) = 7/√4
Hence, the values of the trigonometry functions are sin(α) = 4/7, cos(β) = 4/7, tan(α) = 4/√33, cot(β) = 4/√33, sec(α) = 7/√33 and sec(β) = 7/√4
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Answer:
The circumference for <em>circle a</em> is m.
The circumference for <em>circle b</em> is m.
The relationship between the radius of a circle and the circumference (the distance around the circle) is constant and is the same for all circles and can be written as or, in a less familiar form,
. The number
is constant for all circles and has infinite digits,
.
Step-by-step explanation:
The <em>circumference</em> of a circle is given by:
[1]
Where
is the circle's circumference.
is the radius of the circle.
And
is a constant value (explained below)
We can say that <em>the distance around the circle</em> is the circle's <em>circumference</em>.
The circumferences of the two circles given are:
Circle a, with radius equals to 21 meters ().
Using [1], using four decimals for , we have:
m
m
Then, the circumference for <em>circle a</em> is m.
Circle b, with radius equals to 28 meters ().
m
m
And, the circumference for <em>circle b</em> is m.
We know that
That is, the diameter of the circle is twice its radius.
Then, if we take the distance around the circle and we divided it by
This ratio, that is, the relationship between the distance around the circle (circumference) and <em>the diameter</em> of a circle is and is constant for all circles. This result is called the
number, which is, approximately,
(it has infinite number of digits).
We can observe that the relationship between the radius of a circle and the circumference is also constant:
However, this relationship is .
We can rewrite it as
And it is also constant.